Related papers: Two classes of integral operators over the Siegel …
This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular…
In this paper, we study the $L^{2}$-boundedness and $L^{2}$-compactness of a class of $h$-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to $0)$.
We introduce and study the Bourgain index of an operator between two Banach spaces. In particular, we study the Bourgain $\ell_p$ and $c_0$ indices of an operator. Several estimates for finite and infinite direct sums are established. We…
We give sufficient conditions on an operator space $E$ and on a semigroup of operators on a von Neumann algebra $M$ to obtain a bounded analytic or a $R$-analytic semigroup $(T_t \otimes Id_E)_{t \geq 0}$ on the vector valued noncommutative…
In this paper we investigate the mapping properties of periodic Fourier integral operators in $L^p(\mathbb{T}^n)$-spaces. The operators considered are associated to periodic symbols (with limited regularity) in the sense of Ruzhansky and…
In this article, we characterize the bounded and the compact multiplication operators between distinct iterated logarithmic Lipschitz spaces, and between the Lipschitz space and an iterated logarithmic Lipschitz space of an infinite tree.…
In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear…
A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen…
We establish two-weight norm inequalities for singular integral operators defined on spaces of homogeneous type. We do so first when the weights satisfy a double bump condition and then when the weights satisfy separated logarithmic bump…
In this paper we investigate compactness of weighted Lambert type operators between two Lp spaces
In this article we investigate $L^p$ boundedness of the spherical maximal operator $\mathfrak{m}^\alpha$ of (complex) order $\alpha$ on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, which was introduced and studied by El Kohen. We…
Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…
We prove that a large class of operators, which arise as the projections of martingale transforms of stochastic integrals with respect to Brownian motion, as well as other closely related operators, are in fact Calder\'on--Zygmund…
In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.
It is known that Fourier integral operators arising when solving Schr\"odinger-type operators are bounded on the modulation spaces $\cM^{p,q}$, for $1\leq p=q\leq\infty$, provided their symbols belong to the Sj\"ostrand class…
We discuss $\mathrm{L}^p$ fiber spaces which appear, e.g., as extrapolation spaces of unbounded multiplication operators which in turn are motivated, for instance, by non-autonomous evolution equations.
For two dimensional Schr\"odinger operator $H$ with point interactions, We prove that wave operators of scattering for the pair $(H,H_0)$, $H_0$ being the free Schr\"odinger operator, are bounded in the Lebesgue space $L^p(\R^2)$ for…
In this paper, we obtain an isometry between the Fock-Sobolev space and the Gauss-Sobolev space. As an application, we use multipliers on the Gauss-Sobolev space to characterize the boundedness of an integral operator on the Fock-Sobolev…
In this paper, we develop a semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we…
We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…